Pipes and pipe joints

Contents
1 Notations 2
2 Stresses in Pipes 3
3 Design of Pipes 3
3.1 Inside diameter of the pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Wall thickness of the pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 Pipe Joints 4
5 Standard Pipe Flanges for Steam 7
6 Hydraulic Pipe Joint for High Pressures 8
7 Design of Circular Flanged Pipe Joint 8
8 Design of Oval Flanged Pipe Joint 9
9 Design of Square Flanged Pipe Joint 10
10 Examples 11
10.1 Stresses in Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
10.2 Design of Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
10.3 Design of Circular Flanged Pipe Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
10.4 Design of Oval Flanged Pipe Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
10.5 Design of Square Flanged Pipe Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11 References 18
12 Contacts 18

1 Notations
• p = Internal fluid pressure in the pipe
• ri = Inner radius of the pipe.
• ro = Outer radius of the pipe.
• R = Internal radius of the pipe.
• v = Velocity of fluid flowing per minute.
• Q = Quantity of fluid carried per minute.
• ηl = Efficiency of longitudinal joint.
• n = Number of bolts.
• dc = Core diameter of the bolts.
• σt = Permissible stress for the material of the bolts.
• σb = Bending or tensile stress for the flange material.
• Z = Section modulus of the cross-section of the flange.
• D = Internal diameter of the pipe.
• D1 =Outside diameter of the packing.
• b = Width of the flange at the section X-X.
• tf = Thickness of the flange.

2 Stresses in Pipes
According to Lame’s equation, tangential stress at any radius x,
σt =
pr2
i
r2
o − r2
i
1 +
r2
o
x2
and radial stress at any radius x,
σr =
pr2
i
r2
o − r2
i
1 −
r2
o
x2
The maximum tangential stress at the inner surface of the pipe,
σt(max) =
p [r2
o + r2
i ]
r2
o − r2
i
and minimum tangential stress at the outer surface of the pipe,
σt(min) =
2pr2
i
r2
o − r2
i
The maximum radial stress at the inner surface,
σr(max) = −p (compressive)
and minimum radial stress at the outer surface of the pipe,
σr(min) = 0
The thick cylindrical formula may be applied when
1. the variation of stress across the thickness of the pipe is taken into account,
2. the internal diameter of the pipe (D) is less than twenty times its wall thickness (t), i.e. D/t < 20, and
3. the allowable stress (σt) is less than six times the pressure inside the pipe (p) i.e. σt/p < 6.
According to thick cylindrical formula (Lame’s equation), wall thickness of pipe,
t = R
σt + p
σt − p
− 1
3 Design of Pipes
3.1 Inside diameter of the pipe
D =
4
π
Q
v
= 1.13
Q
v

3.2 Wall thickness of the pipe
After deciding upon the inside diameter of the pipe, the thickness of the wall (t) in order to withstand the
internal ﬂuid pressure (p) may be obtained by using thin cylindrical or thick cylindrical formula.
The thin cylindrical formula may be applied when
1. the stress across the section of the pipe is uniform,
2. the internal diameter of the pipe (D) is more than twenty times its wall thickness (t), i.e. D/t > 20, and
3. the allowable stress (σt) is more than six times the pressure inside the pipe (p), i.e. σt/p > 6.
According to thin cylindrical formula, wall thickness of pipe,
t =
pD
2σt
or
pD
2σtηl
A little consideration will show that the thickness of wall as obtained by the above relation is too small. Therefore
for the design of pipes, a certain constant is added to the above relation. Now the relation may be written as
t =
pD
2σt
+ C
4 Pipe Joints
There are various forms of pipe joints used in practice, but most common of them are discussed below.
1. Socket or a coupler joint.
The most common method of joining pipes is by means of a socket or a coupler. A socket is a small piece of
pipe threaded inside. It is screwed on half way on the threaded end of one pipe and the other pipe is then
screwed in the remaining half of socket. In order to prevent leakage, jute or hemp is wound around the
threads at the end of each pipe. This type of joint is mostly used for pipes carrying water at low pressure
and where the overall smallness of size is most essential.
Figure 1: Socket or coupler joint.
2. Nipple joint.
In this type of joint, a nipple which is a small piece of pipe threaded outside is screwed in the internally
threaded end of each pipe. The disadvantage of this joint is that it reduces the area of ﬂow.
Figure 2: Nipple joint.

3. Union joint.
In order to disengage pipes joined by a socket, it is necessary to unscrew pipe from one end. This is
sometimes inconvenient when pipes are long.
Figure 3: Union joint.
4. Spigot and socket joint.
A spigot and socket joint is chiefly used for pipes which are buried in the earth. Some pipe lines are laid
straight as far as possible. One of the important features of this joint is its flexibility as it adopts itself to
small changes in level due to settlement of earth which takes place due to climate and other conditions.
In this type of joint, the spigot end of one pipe fits into the socket end of the other pipe. The remaining
space between the two is filled with a jute rope and a ring of lead. When the lead solidifies, it is caulked-in
tightly.
Figure 4: Spigot and socket joint.
5. Expansion joint.
The pipes carrying steam at high pressures are usually joined by means of expansion joint. This joint is
used in steam pipes to take up expansion and contraction of pipe line due to change of temperature.
In order to allow for change in length, steam pipes are not rigidly clamped but supported on rollers. The
rollers may be arranged on wall bracket, hangers or floor stands. The expansion bends are useful in a long
pipe line. These pipe bends will spring in either direction and readily accommodate themselves to small
movements of the actual pipe ends to which they are attached.
Figure 5: Expansion bends.
The copper corrugated expansion joint, as shown in Fig. 8.7 (a), is used on short lines and is satisfactory
for limited service. An expansion joint (also known as gland and stuffing box arrangement), is the most
satisfactory when the pipes are well supported and cannot sag.

Figure 6: Expansion joints.
6. Flanged joint.
It is one of the most widely used pipe joint. A flanged joint may be made with flanges cast integral with
the pipes or loose flanges welded or screwed. Fig. 11 shows two cast iron pipes with integral flanges at
their ends. The flanges are connected by means of bolts. The flanges have seen standardised for pressures
upto 2N/mm2
. The flange faces are machined to ensure correct alignment of the pipes. The joint may
be made leakproof by placing a gasket of soft material, rubber or convass between the flanges. The flanges
are made thicker than the pipe walls, for strength. The pipes may be strengthened for high pressure duty
by increasing the thickness of pipe for a short length from the flange.
Figure 7: Flanged joint.
For even high pressure and for large diameters, the flanges are further strengthened by ribs or stiffners.
The ribs are placed between the bolt holes.

For larger size pipes, separate loose flanges screwed on the pipes are used instead of integral flanges.
Figure 9:
7. Hydraulic pipe joint.
This type of joint has oval flanges and are fastened by means of two bolts. The oval flanges are usually
used for small pipes, upto 175 mm diameter. The flanges are generally cast integral with the pipe ends.
Such joints are used to carry fluid pressure varying from 5 to 14N/mm2
. Such a high pressure is found in
hydraulic applications like riveting, pressing, lifts etc. The hydraulic machines used in these installations
are pumps, accumulators, intensifiers etc.
Figure 10: Hydraulic pipe joint.
5 Standard Pipe Flanges for Steam
The Indian boiler regulations (I.B.R.) 1950 (revised 1961) have standardised all dimensions o pipe and flanges
based upon steam pressure. They have been divided into five classes as follows:
1. Class I: For steam pressures up to 0.35 N/mm2
and water pressures up to 1.4 N/mm2
. This is not
suitable for feed pipes and shocks.
2. Class II: For steam pressures over 0.35 N/mm2
but not exceeding 0.7 N/mm2
.
3. Class III: For steam pressures over 0.7 N/mm2
.
4. Class IV: For steam pressures over 1.05 N/mm2
.
5. Class V: For steam pressures from 1.75 N/mm2
to 2.45 N/mm2
.
According to I.B.R., it is desirable that for classes II, III, IV and V, the diameter of flanges, diameter of bolt
circles and number of bolts should be identical and that difference should consist in variations of the thickness

of flanges and diameter of bolts only. The I.B.R. also recommends that all nuts should be chamfered on the
side bearing on the flange and that the bearing surfaces of the flanges, heads and nuts should be true. The
number of bolts in all cases should be a multiple of four. The I.B.R. recommends that for 12.5 mm and 15 mm
bolts, the bolt holes should be 1.5 mm larger and for higher sizes of bolts, the bolt holes should be 3 mm larger.
All dimensions for pipe flanges having internal diameters 1.25 mm to 600 mm are standardised for the above
mentioned classes (I to V). The flanged tees, bends are also standardised.
Note: As soon as the size of pipe is determined, the rest of the dimensions for the flanges, bolts, bolt holes,
thickness of pipe may be fixed from standard tables. In practice, dimensions are not calculated on a rational
basis. The standards are evolved on the basis of long practical experience, suitability and interchangeability.
The calculated dimensions as discussed in the previous articles do not agree with the standards. It is of
academic interest only that the students should know how to use fundamental principles in determining various
dimensions e.g. wall thickness of pipe, size and number of bolts, flange thickness. The rest of the dimensions
may be obtained from standard tables or by empirical relations.
6 Hydraulic Pipe Joint for High Pressures
The pipes and pipe joints for high fluid pressure are classified as follows:
1. For hydraulic pressures up to 8.4 N/mm2
and pipe bore from 50 mm to 175 mm, the flanges and pipes
are cast integrally from remelted cast iron. The flanges are made elliptical and secured by two bolts. The
proportions of these pipe joints have been standardised from 50 mm to 175 mm, the bore increasing by 25
mm. This category is further split up into two classes:
(a) Class A: For fluid pressures from 5 to 6.3 N/mm2
, and
(b) Class B: For fluid pressures from 6.3 to 8.4 N/mm2
.
The flanges in each of the above classes may be of two types. Type I is suitable for pipes of 50 to 100 mm
bore in class A, and for 50 to 175 mm bore in class B. The flanges of type II are stronger than those of
Type I and are usually set well back on the pipe.
2. For pressures above 8.4 N/mm2
with bores of 50 mm or below, the piping is of wrought steel, solid drawn,
seamless or rolled. The flanges may be of cast iron, steel mixture or forged steel. These are screwed or
welded on to the pipe and are square in elevation secured by four bolts. These joints are made for pipe
bores 12.5 mm to 50 mm rising in increment of 3 mm from 12.5 to 17.5 mm and by 6 mm from 17.5 to 50
mm. The flanges and pipes in this category are strong enough for service under pressures ranging up to
47.5 N/mm2
.
Notes: The hydraulic pipe joints for high pressures differ from those used for low or medium pressure in the
following ways:
1. The flanges used for high pressure hydraulic pipe joints are heavy oval or square in form, They use two
or four bolts which is a great advantage while assembling and disassembling the joint especially in narrow
space.
2. The bolt holes are made square with sufficient clearance to accommodate square bolt heads and to allow
for small movements due to setting of the joint.
3. The surfaces forming the joint make contact only through a gutta-percha ring on the small area provided
by the spigot and recess. The tightening up of the bolts squeezes the ring into a triangular shape and
makes a perfectly tight joint capable of withstanding pressure up to 47.5 N/mm2
.
4. In case of oval and square flanged pipe joints, the condition of bending is very clearly defined due to the
flanges being set back on the pipe and thickness of the flange may be accurately determined to withstand
the bending action due to tightening of bolts.
7 Design of Circular Flanged Pipe Joint
Consider a circular flanged pipe joint as shown in Fig. 7. In designing such joints, it is assumed that the fluid
pressure acts in between the flanges and tends to separate them with a pressure existing at the point of leaking.
The bolts are required to take up tensile stress in order to keep the flanges together. The effective diameter on
which the fluid pressure acts, just at the point of leaking, is the diameter of a circle touching the bolt holes.
Let this diameter be D1. If d1 is the diameter of bolt hole and Dp is the pitch circle diameter, then
D1 = Dp − d1

∴ Force trying to separate the two flanges,
f =
π
d
D2
1p
∴ Resistance to tearing of bolts
=
π
4
d2
c σt n
The number of bolts should be even because of the symmetry of the section.
The circumferential pitch of the bolts is given by
pc =
πDp
n
In order to make the joint leakproof, the value of pc should be between 20
√
d1 to 30
√
d1 where d1 is the diameter
of the bolt hole. Also a bolt of less than 16 mm diameter should never be used to make the joint leakproof.
In this it is assumed that each of the bolt supports one segment. The effect of joining of these segments on the
stresses induced is neglected. The bending moment is taken about the section X-X, which is tangential to the
outside of the pipe. Let the width of this segment is x and the distance of this section from the center of the
bolt is y. ∴ Bending moment on each bolt due to the force F
=
F
n
y
and resisting moment on the flange
= σb Z
Z =
1
6
x t2
f
The dimensions of the flange may be fixed as follows:
Nominal diameter of bolts, d = 0.75 t + 10 mm
Number of bolts, n = 0.0275 D + 1.6 ...(D is in mm)
Thickness of flange, tf = 1.5 t + 3 mm
Width of flange, B = 2.3 d
Outside diameter of flange, Do = D + 2t + 2B
Pitch circle diameter of bolts, Dp = D + 2t + 2d + 12 mm
The pipes may be strengthened by providing greater thickness near the flanges equal to
t+tf
2
8 Design of Oval Flanged Pipe Joint
Consider an oval flanged pipe joint as shown in Fig. 10. A spigot and socket is provided for locating the pipe
bore in a straight line. A packing of trapezoidal section is used to make the joint leak proof. The thickness of
the pipe is obtained as discussed previously.
The force trying to separate the two flanges has to be resisted by the stress produced in the bolts. If a length of
pipe, having its ends closed somewhere along its length, be considered, then the force separating the two flanges
due to fluid pressure is given by
F1 =
π
4
D2
p
The packing has also to be compressed to make the joint leakproof. The intensity of pressure should be greater
than the pressure of the fluid inside the pipe. For the purposes of calculations, it is assumed that the packing
material is compressed to the same pressure as that of inside the pipe. Therefore the force tending to separate
the flanges due to pressure in the packing is given by
F2 =
π
4
D2
1 − D2
2 p
∴ Total force trying to separate the two flanges,
F = F1 + F2
=
π
4
D2
p +
π
4
D2
1 − D2
2 p
Since an oval flange is fastened by means of two bolts, therefore load taken up by each bolt is Fb = F/2 . If dc
is the core diameter of the bolts, then
Fb =
π
4
d2
c σtb

where σtb is the allowable tensile stress for the bolt material. The value of σtb is usually kept low to allow for
initial tightening stress in the bolts. After the core diameter is obtained, then the nominal diameter of the bolts
is chosen from tables(In the absence of tables, nominal diameter = Core diameter
0.84
). It may be noted that bolts
of less than 12 mm diameter should never be used for hydraulic pipes, because very heavy initial tightening
stresses may be induced in smaller bolts. The bolt centers should be as near the center of the pipe as possible to
avoid bending of the flange. But sufficient clearance between the bolt head and pipe surface must be provided
for the tightening of the bolts without damaging the pipe material.
The thickness of the flange is obtained by considering the flange to be under bending stresses due to the forces
acting in one bolt. The maximum bending stress will be induced at the section X-X. The bending moment at
this section is given by
Mxx = Fb e =
F
2
e
Z =
1
6
b t2
f
Using the bending equation, we have
Mxx = σb Z
Fb e = σb
1
6
b t2
f
σb = Permissible bending stress for the flange material.
From the above expression, the value of t f may be obtained, if bis known. The width of the flange is estimated
from the lay out of the flange. The hydraulic joints with oval flanges are known as Armstrong’s pipe joints.
The various dimensions for a hydraulic joint may be obtained by using the following empirical relations:
Nominal diameter of bolts, d = 0.75 t + 10 mm
Thickness of the flange, tf = 1.5 t + 3 mm
Outer diameter of the flange, Do = D + 2t + 4.6 d
Pitch circle diameter, Dp = Do(3 t + 20 mm)
9 Design of Square Flanged Pipe Joint
The design of a square flanged pipe joint is similar to that of an oval flanged pipe joint except that the load has
to be divided into four bolts. The thickness of the flange may be obtained by considering the bending of the
flange about one of the sections A-A, B-B, or C-C.
A little consideration will show that the flange is weakest in bending about section A-A. Therefore the thickness
of the flange is calculated by considering the bending of the flange, about section A-A.

10 Examples
10.1 Stresses in Pipes

10.2 Design of Pipes
10.3 Design of Circular Flanged Pipe Joint

10.4 Design of Oval Flanged Pipe Joint

10.5 Design of Square Flanged Pipe Joint

11 References
1. R.S. KHURMI, J.K. GUPTA, A Textbook Of Machine Design
12 Contacts
mohamed.atyya94@eng-st.cu.edu.eg

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